Quantized average consensus: Discontinuities and hysteresis

It is well known that the consensus problem can be formulated in terms of a stabilization problem. In this note we consider continuous-time average consensus dynamics: We discuss how quantization can be included in the system, and focus on one model in which the agents’ states are communicated through uniform quantizers. Solutions to the resulting system are defined in the Krasowskii sense, and results are given proving their convergence to conditions of practical consensus. To cope with potential chattering phenomena, which may be undesired in the applications, we propose the use of a hysteretic quantizer, and study the convergence properties of the resulting dynamics by a hybrid system approach.